A matrix ring description for cyclic convolutional codes

Heide Gluesing-Luerssen, Fai Lung Tsang

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe the algebraic parameters of the codes in a more accessible way. We show that the existence of such codes with given algebraic parameters can be reduced to the solvability of a modified rook problem. It is our strong belief that the rook problem is always solvable, and we present solutions in particular cases.

Original languageEnglish
Pages (from-to)55-81
Number of pages27
JournalAdvances in Mathematics of Communications
Issue number1
StatePublished - Feb 2008


  • Convolutional codes
  • Cyclic codes
  • Forney indices
  • Skew polynomial rings

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computer Networks and Communications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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